I understand this will sound crazy on first reading but think about it.

Your mom was once young just like you are and she dealt with the same problems you are dealing with. Some parents have very negative feelings about masturbation but nowhere near as negative as they feel about you becoming sexually active with boys. Try to talk to her about it and explain that you want to be able to control your urges without taking the risks of pregnancy. Just ask her how a girl is supposed to deal with it. She may be more understanding than you think.